Given log 10(90) = 1.9542, find log 10(3). Use the relationships among 3, 9, and 90.

Introduction / Context:
This problem uses the factorization of 90 and standard log identities to isolate log 3.

Given Data / Assumptions:

• log 10(90) = 1.9542
• 90 = 9 × 10 = 3^2 × 10

Concept / Approach:
Use log(AB) = log A + log B and power rules to relate log 90 to log 3.

Step-by-Step Solution:

Verification / Alternative check:
Since 3 ≈ 10^0.4771, then 3^2 × 10 ≈ 10^0.9542 × 10 = 10^1.9542 ≈ 90, consistent with the given number.

Why Other Options Are Wrong:
Other decimals do not satisfy 2·log 3 + 1 = 1.9542 when substituted; only 0.4771 does.

Common Pitfalls:
Forgetting that log 10 = 1 or failing to divide by 2 after isolating 2·log 3 are common mistakes.

Final Answer:
0.4771